234.

 (a) Determine the type of cubic lattice to which a given crystal belongs if it has edge length of 290 pm and density is 7.80 g cm^–3. (Molecular mass.= 56 g mol^–1)

(b) Why does zinc oxide exhibit enhanced electrical conductivity on heating?

we know that

$\mathrm{d} =\frac{\mathrm{ZM}}{{\mathrm{a}}^3{\mathrm{N}}_{\mathrm{A}}}$

as we have given 
d= 7.80 g cm^–3.
M=56 g mol^–1
a= 290 pm or a³ =2.43 x10^-23
putting all value in above equation we get,

$$\begin{gathered} \mathrm{Z} =\frac{{\mathrm{a}}^3 \mathrm{x} \mathrm{d} {\mathrm{xN}}_{\mathrm{A}}}{\mathrm{M}} \\ \mathrm{Z}=\frac{ 2.43 \mathrm{x}{10}^{-23} \mathrm{x} 7.80 \mathrm{x}6.022 \mathrm{x}{10}^{23}}{56} =2.03 \end{gathered}$$

hence it belong to bcc crystal lattice.

b) Zinc oxide is white in colour at room temperature. On heating it loses electron and turns yellow in colour. 

$\mathrm{ZnO}\stackrel{∆}{\to } {\mathrm{Zn}}^{2+} +\frac{1}{2}{\mathrm{O}}_2 +2{\mathrm{e}}^{-}$ 

The electron liberate after heating, can act as charge carrier and thus on heating zinc oxide it exhibit electrical conductivity.